George Frey/Reuters
McCray was named the new leader of Access, which includes the Google Fiber internet service, last week.
Recently, The Information speculated that Alphabet may want to sell the Google Fiber business this year and floated CenturyLink as a likely buyer. McCray's position on CenturyLink's board could've been a conflict.
Google Fiber lost its CEO Craig Barratt last year and announced it no longer plans to expand to new cities. Hundreds of Fiber employees have either been laid off or reassigned to other divisions within Alphabet since then.